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Proof step 584 from proof bitsand-cast (previous step)

#(boolvar ' + boolvar0 ' + bits) ≤ # bits1 ∧ boolvar ' + boolvar0 ' + bits ≠ [] ∧ ¬ (boolvar ' + boolvar0 ' + bits).first, # bits1 = 2 + # bits, sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ bits3 = [], lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, boolvar ' + boolvar0 ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits3 + bits1))), n = 0, boolvar ↔ boolvar0, bits3 + bits1 = [], boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 585:
sgn(mklist(false, n - 1) + false ' + true ' + bits) = false ' + true ' + bits, # bits1 = 2 + # bits ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(false, n - 1)) + false ' + true ' + bits, bits3 + bits1))), bits3 = [], bits3 + bits1 = []

Rule argument

Additional information

Used simplifier rules: ⊦ boolvar ∈ boolvar0 ' ↔ boolvar ↔ boolvar0;% ⊦ boolvar ∈ bits + bits0 ↔ ¬ ¬(boolvar ∈ bits ∨ boolvar ∈ bits0);% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits;% ⊦ bits = bits0 + boolvar ' + bits1 → boolvar ∈ bits; (forward)% ⊦ boolvar ' + bits = bits0 → boolvar ∈ bits0; (forward)% ⊦ m ≤ m;% ⊦ (boolvar ' + bits).first ↔ boolvar;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ boolvar ' + bits ≠ [];